In my hometown, Sheffield, there was a shot -down Messerschmidt parked in the town centre as a propaganda tool and fund raising initiative. People paid a few pence to sit in it and buy a stamp that was stuck to the fuselage, the money collected going to a fund called 'Wings For Victory ', which raised cash for the war e effort. My Great -Uncle told me the stamps often had personal messages to Hitler written on them by the purchasers!

EDIT: More info here.

Especially during the summer of 1940 when an invasion appeared likely and the UK was suffering from a shortage of weaponry due to much of their equipment being abandoned at Dunkirk.

Keep in mind the scale of a western military of that era. Dunkirk only evacuated an expeditionary force, the equipment left behind was replaced in short order.

Enemy equipment isn't easily integrated as ammo is of a different size. Some was used individually but not to a strategic extent.